利用M-H算法求解Logistic回归模型参数的贝叶斯估计

Bayesian Estimation of Using M-H Algorithm to Solve Logistic Regression Model Parameters

文章以航天飞机在不同温度下发射密封圈的失效数据为例,采用随机游动与变量变换M-H算法获得Logistic回归模型参数的后验分布样本并进行贝叶斯分析。同时,进行蒙特卡洛模拟,通过样本轨迹图、直方图、自相关系数图等考查M-H算法的抽样表现,并讨论每种抽样方法的优缺点与提高措施。结果表明:先验分布的选取直接影响贝叶斯估计效果,有先验信息的M-H算法估计的标准差比无先验信息的M-H算法要精确,但随着样本容量增大,趋势在减少,适当的建议分布与变量变换可大大提高M-H算法的抽样效率。

This paper takes the failure data of space shuttle launching sealing rings at different temperatures for example, and conducts Bayesian analysis by adopting random walk and variable transformation M-H algorithm to obtain the posterior distri- bution samples of logistic regression model parameters. Meanwhile, the paper makes a Monte-Carlo simulation, and investigates the sampling performance of M-H algorithm by use of sample trajectory diagram, histogram and autocorrelation coefficient graph and so forth. Finally the paper also discusses the advantages and disadvantages of each sampling method. The analysis result is shown as follows： the selection of the priori distribution directly affects the Bayesian estimation effect; the standard deviation of the M-H algorithm with a priori information is better than the M-H algorithm without prior information, but with the increase of the sample capacity, the trend is decreasing. Appropriate proposed distribution and variable transformation can greatly improve sampiing efficiency of M-H algorithm